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We study three-dimensional non-linear models of vector and vector-spinorGoldstone fields associated with the spontaneous breaking of certainhigher-spin counterparts of supersymmetry whose Lagrangians are of aVolkov-Akulov type. Goldstone fields in these models transform non-linearlyunder the spontaneously broken rigid symmetries. We find that the leading termin the action of the vector Goldstone model is the Abelian Chern-Simons actionwhose gauge symmetry is broken by a quartic term. As a result, the model has apropagating degree of freedom which, in a decoupling limit, is a quarticGalileon scalar field. The vector-spinor goldstino model turns out to be anon-linear generalization of the three-dimensional Rarita-Schwinger action. Incontrast to the vector Goldstone case, this non-linear model retains the gaugesymmetry of the Rarita-Schwinger action and eventually reduces to the latter bya non-linear field redefinition. We thus find that the free Rarita-Schwingeraction is invariant under a hidden rigid supersymmetry generated by fermionicvector-spinor operators and acting non-linearly on the Rarita-Schwingergoldstino.

Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?